Question

Find the natural frequency of the system shown in figure. The pulleys are smooth and mass less.

Answer 1

If the mass M is displaced by x from its mean position each spring further stretches by 2x.
Net restoring force
$F=-8kx$
$\therefore$ $M.a=-8kx$
$f=\frac{1}{2\pi }\sqrt{\left|\frac{a}{x}\right|}$
$=\frac{1}{2\pi }\sqrt{\frac{8k}{M}}$
$=\frac{1}{\pi }\sqrt{\frac{2k}{M}}$